Notwithstanding the above criticisms standard deviation (the square root of variance) is commonly used in finance as a measure of risk The reasons are:
1. If a variable is normally distributed, its mean and standard deviation contain all the information about its probability distribution. The probability that a particular outcome will be above or blow, a specified value can be determined. 68.3% of the values fall within a band of one standard deviation on either side of the arithmetic mean. This % increases to 95% for 2 standard deviations and 99% for 3 S.D.s.
2. If the utility of money is represented by a quadratic function (a function commonly suggested to represent diminishing marginal utility of wealth),then the expected utility is a function of mean and standard deviation.
3. S.D is analytically more easily tractable.